Ratio and Proportion
Research Clip
Posted on March 11, 2013
Summary clip for Ratio and Proportion
A proportion is a relationship of equality between two ratios. Research on students’
understanding of ratio and proportion suggests that developing a conceptual understanding
of ratio relationships includes the following:
• Learning to attend to two quantities simultaneously
• Forming a multiplicative comparison of two quantities; for example, comparing a
25-inch rope to a 10-inch rope by understanding that the first rope is 2.5 times as
long as the second
• Forming a composed unit, such as a 3:2 unit to describe a class that has 3 girls for
every 2 boys, and iterating (repeating) and partitioning (breaking into equal-size
parts) the unit
• Creating a family of equivalent ratios by iterating and partitioning or by using
multiplication and division
Studies have found that a strong foundation in proportional reasoning can support students’
understanding of linear functions and graphs, linear equations in the form y = mx and
y = mx + b, and measurement situations. Teachers can promote students’ proportional
reasoning capacities by balancing skills and concepts and by delaying the instruction
of the cross-multiplication algorithm until students have already gained experience with
forming ratios and understanding proportions as an equivalence of ratios.
Based on Teaching Ratio and Proportion in the Middle Grades
The views expressed or implied in this publication, unless otherwise noted, should not be interpreted as official positions
of the Council.
Copyright © 2013 by The National Council of Teachers of Mathematics, 1906 Association Drive, Reston, VA 20191-1502,
Tel: (703) 620-9840, Fax: (703) 476-2690, www.nctm.org.